CN110298082B - Method for obtaining coating bidirectional reflection distribution function simulation parameters through imaging method - Google Patents

Method for obtaining coating bidirectional reflection distribution function simulation parameters through imaging method Download PDF

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CN110298082B
CN110298082B CN201910484740.XA CN201910484740A CN110298082B CN 110298082 B CN110298082 B CN 110298082B CN 201910484740 A CN201910484740 A CN 201910484740A CN 110298082 B CN110298082 B CN 110298082B
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朱长林
王艳春
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Harbin Xinguang Photoelectric Technology Co ltd
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Abstract

The invention provides a method for acquiring a bidirectional reflection distribution function simulation parameter of a coating by an imaging method, aiming at solving the defects that a BRDF (bidirectional reflectance distribution function) measuring method in the technology can not meet the input parameter requirement of a real-time simulation platform, but also can meet the measuring precision, and the method comprises the following steps: placing the standard ball with the coating on the surface under a parallel light source to form a shadow; imaging the standard ball for multiple times through the imaging device, and recording the distance between the imaging device, the standard ball and the shadow every time of imaging; calculating the cosine of an included angle between the reverse direction J of the incident light and the emergent light O according to the distance between the imaging equipment, the standard ball and the shadow; calculating the pixel position coordinates of the circle center according to the picture acquired by the imaging equipment; calculating the azimuth angle beta of the J in the picture plane; calculating the azimuth angle of the macroscopic normal direction Z of each pixel point in the image circle and the included angle gamma between Z and O; and finally fitting by an analytical formula. The method is suitable for target material simulation of the semi-physical simulation platform.

Description

Method for obtaining coating bidirectional reflection distribution function simulation parameters through imaging method
Technical Field
The invention relates to the field of semi-physical simulation systems, in particular to a method for acquiring a bidirectional reflection distribution function simulation parameter of a coating by an imaging method.
Background
The target material simulation is an important component of visual simulation such as a semi-physical visual simulation system. The main work of the target material simulation is to implement its BRDF (bidirectional reflectance distribution function) with computer code and programs. The simulation system has low requirements on simulation input parameters, and has two main reasons: firstly, the final result of the visual simulation is embodied in the form of a picture and is output in a color or black-and-white manner through a display with at most 256 brightness levels after being gained, so that the ratio of the actual output brightness error to the maximum possible value is about 0.5/255-0.2%; secondly, in many engineering practices it is not required that the final output brightness has such a high accuracy. The requirement for position accuracy in a semi-physical simulation system for checking a target tracking algorithm exceeds the requirement for brightness color level accuracy. The gray scale can be deviated by about 5 color levels without influencing the practical use of the system. Thus, the relative error requirements of the semi-physical visual simulation system on the simulation result and the input parameters are about 1%.
As a general medium for reflecting the reflection characteristics of materials, a Bidirectional Reflection Distribution Function (BRDF) describes the distribution of energy flow reflected from any incident direction to any emergent direction, and is equal to the ratio of the radiance of emergent light in the emergent direction to the radiance of incident light in the incident direction. The basic test method of the traditional BRDF tester is to place a small piece of plane material to be tested at a reflection point, adjust the direction of a parallel incident light source in a darkroom, and then measure the radiance in each possible emergent light direction and compare the radiance with the incident illumination. In the method, the material to be tested needs to be slowly rotated to perform point-by-point scanning on the angle, so that time and labor are wasted, and a harsh experimental environment needs to be maintained for a long time. The precision is high, but the equipment price is expensive, so that the engineering practice of visual image simulation with low precision requirement is not facilitated. For example, the comprehensive error of a high-precision BRDF test solution developed in 2014 by Anhui optical precision machinery research of Chinese academy of sciences is about 0.66%, and is obviously superior to the requirement of semi-physical visual simulation error.
However, the hardware-in-the-loop simulation system often has high requirements on software real-time performance, and simulation images need to be displayed at a fast refresh rate. The general engineering requirement is at least above 100fps, that is, more than 100 pictures are displayed per second. And the picture content needs to be changed correspondingly according to the observation direction of the user or the device to be tested. To meet such high demands, simulation techniques utilizing hardware acceleration have even appeared in recent years. In a real-time simulation platform such as the phantom four, in order to improve the real-time performance, numerical BRDF point-by-point data is not adopted but is replaced by a parameterized formula, and the reflection characteristics of the material can be described by using a small number of parameters. The results of a professional BRDF tester are not directly applicable to such application scenarios.
BRDF parameterization studies for complex rough surfaces have been in existence, and various analytical models of BRDF are widely used in various aspects of visual simulation. In 1967, Torrance and Sparrow abstracted micro-surface primitive models to explain the reflection theory of rough surfaces, they expressed the body part of BRDF as the product of fresnel reflectivity (F-function), micro-surface primitive normal distribution (D-function), geometric shading factor (G-function), and the simulation parameters proposed by phantom four were mainly metallic, roughness and spectral factors. However, a method for measuring the BRDF parameter is lacked, which can not only meet the input requirement of a real-time simulation platform, but also meet higher measurement accuracy.
Therefore, a new method for obtaining simulation parameters of a reflection distribution function is needed to overcome the defects in the prior art.
Disclosure of Invention
The invention aims to overcome the defect that the BRDF measuring method in the technology can not only meet the input parameter requirement of a real-time simulation platform, but also meet the measuring precision.
According to a first aspect of the invention, there is provided a method for obtaining a simulation parameter of a bidirectional reflectance distribution function of a coating by an imaging method, comprising a measuring step, a calculating step before fitting, and a fitting step, wherein,
the measuring step comprises: placing the standard ball with the coating on the surface under a parallel light source to form a shadow;
imaging the standard ball for multiple times through the imaging device, and recording the distance between the imaging device, the standard ball and the shadow every time of imaging; the calculating step before fitting comprises: calculating the cosine of an included angle between the reverse direction J of the incident light and the emergent light O according to the distance between the imaging equipment, the standard ball and the shadow; calculating the pixel position coordinates of the circle center according to the picture acquired by the imaging equipment; calculating the azimuth angle beta of the J in the picture plane; calculating the azimuth angle phi of the macroscopic normal direction Z of each pixel point in the image circle and the included angle gamma between Z and O; the fitting step comprises: fitting the brightness value L by the following analytical formula to obtain the metal M, the roughness R and the spectral factor F0The fitting result of (a):
L=L0+L1+L2+L3+L4
L0is the spontaneous emission of a standard sphere; l is1Primary source radiation reflected by a standard sphere; l is2Photographer radiation reflected off of a standard sphere; l is3Fixed dim background radiation reflected by standard sphere;L4Is the spontaneous emission of air on the standard ball to imaging device path.
Preferably, L0、L1、L2、L3And L4The calculation formula of (2) is as follows:
Figure GDA0002795043560000031
Figure GDA0002795043560000032
Figure GDA0002795043560000033
Figure GDA0002795043560000034
Figure GDA0002795043560000035
wherein B (I, O, Z) is a parameterized formula of BRDF; t isa、TbTemperatures recorded for air and standard ball, respectively; p (-) is Planck's formula; kappa is an extinction coefficient; sabIs the shooting distance of the imaging device to the standard ball; c1For shading factor, when the main light source is turned on for shooting C11, shading shooting C1Taking 0; a. the0、A1、A2、A3And A4Are all scaling coefficients that can be determined by fitting.
Preferably, the parameterized formula of the BRDF is of the specific form:
Figure GDA0002795043560000036
F(O,H)=F0+(1-F0)2(-5.55473<O,H>-6.98316<O,H>)
Figure GDA0002795043560000037
α=R2
G(I,O,H)=G1(I,H)G2(O,H)
Figure GDA0002795043560000041
Figure GDA0002795043560000042
wherein M is metallic and is used for describing the proportion of the metallic micro surface element; r is roughness, which is used for representing the roughness of the surface; f0Is a spectral factor used to characterize the reflectance of light rays incident perpendicularly to the surface.
Preferably, when the imaging device is a visible light imaging device, before the fitting step, the method further comprises the step of discarding the more than 255 levels of picture brightness saturation pixel data in the visible light band.
Preferably, the imaging device is an infrared imaging device or a visible light imaging device.
The invention has the beneficial effects that: 1. the main results obtained by final fitting are metallicity, roughness and spectral factors, and the input requirements of a real-time simulation platform including unreal four are met; 2. through the verification of the experimental results in tables 1 to 4, the relative error of the fitting result is very small, the simulation precision requirement can be met, and the method can be applied to visual simulation engineering. One application of the invention is that the parameter results obtained by fitting can be input into a simulation platform to simulate the effect of a certain material under the influence of reflected light.
Other features of the present invention and advantages thereof will become apparent from the following detailed description of exemplary embodiments thereof, which proceeds with reference to the accompanying drawings.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of the invention.
FIG. 1 is a flow chart of one embodiment of the present invention;
FIGS. 2(a) to 2(d) are simulation results of an embodiment of the present invention; wherein FIG. 2(a) is the simulation effect for the 0.45 micron band; FIG. 2(b) is a simulation effect of the 0.55 μm band; FIG. 2(c) is the simulation effect of the 0.65 micron band; fig. 2(d) shows the simulation effect of the 10-micron band.
Detailed Description
Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that: the relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise.
The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.
Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate.
In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
The invention discloses a method for obtaining coating bidirectional reflection distribution function simulation parameters by an imaging method, which comprises a measuring step S1, a calculating step S2 before fitting and a fitting step S3, as shown in figure 1, wherein,
the measurement step S1 includes:
S1A, placing the standard ball with the coating on the surface under a parallel light source to form a shadow;
S1B, imaging the standard ball for multiple times through the imaging device, and recording the distance between the imaging device, the standard ball and the shadow every time of imaging;
the pre-fitting calculation step S2 includes:
calculating the cosine of an included angle between the reverse direction J of the incident light and the emergent light O according to the distance between the imaging equipment, the standard ball and the shadow; calculating the pixel position coordinates of the circle center according to the picture acquired by the imaging equipment; calculating the azimuth angle beta of the J in the picture plane; calculating the azimuth angle phi of the macroscopic normal direction Z of each pixel point in the image circle and the included angle gamma between Z and O;
the fitting step S3 includes:
fitting the brightness value L by the following analytical formula to obtain the metal M, the roughness R and the spectral factor F0The fitting result of (a):
L=L0+L1+L2+L3+L4
L0is the spontaneous emission of a standard sphere; l is1Primary source radiation reflected by a standard sphere; l is2Photographer radiation reflected off of a standard sphere; l is3Fixed dim background radiation reflected off of a standard sphere; l is4Is the spontaneous emission of air on the standard ball to imaging device path.
After fitting, the required simulation parameters can be obtained. The resulting simulation parameters include, but are not limited to: metallic M, roughness R, spectral factor F0An extinction coefficient k and a scaling coefficient a for expressing factors related to camera imaging gain and the like.
It should be noted that there are various ways how to perform L fitting, and the calculation formulas of various types of radiation constituting L, such as spontaneous radiation of a sphere, are all described in textbooks, and the difference of the specifically used formulas only affects the approximation degree, but the main technical contribution of the present invention lies in the measurement process, that is, necessary parameters are quickly obtained by the imaging device, and then the fitting result conforming to the input condition of the simulation platform is obtained by fitting. L is0、L1、L2、L3、L4Slight changes in the form of the formula or fitting of (a) do not affect the technical contribution of the present invention. The person skilled in the art can freely select the fitting mode and the approximate calculation formula of various radiations according to actual needs, which does not affect the implementation of the invention.
One embodiment of the measuring step S1 is as follows:
in order to quickly obtain the BRDF parameter value of the coating material, a standard ball with a coating on the surface can be firstly placed under a parallel light source. Thus, various possibilities arise between the macro normals of the material at various locations and the angle of incidence. And the order records a small amount of distance information, the angle can be directly extracted from the pixel position on the image photo. Then, the imaging device is used for shooting at various angles, and a numerical function to be fitted, namely the change of brightness along with the position, is actually obtained. In the case that a specific form of a Torrance type BRDF parameterized formula is known, a formula of the parameter with the brightness varying with the position is provided. And fitting the numerical function by using the formula related to BRDF (bidirectional reflectance distribution function), so as to obtain parameter values which can sufficiently meet the requirement of image simulation precision.
In the experiment, the stray visible light source in the laboratory is turned off, and the stray radiation under the detection wave band is reduced as much as possible. For example, if the detection band is the infrared band, the laboratory temperature should be minimized. The main light source is turned on and directed at the standard ball after the coating is cured and causes the standard ball to form a shadow on the laboratory wall or other back plate. And imaging the standard ball at each position far away from the light-receiving hemisphere by using imaging equipment with a detection waveband, and simultaneously recording the distance between the camera, the standard ball and the shadow every time of imaging. If the detection waveband is an infrared waveband, a thermometer is used for recording the temperature of a laboratory, and a temperature measuring gun is used for recording the surface temperature of the standard ball. And in the infrared band, the position of the camera and the standard ball is kept to be in a non-shielded state for imaging once after the main light source is turned on for imaging once. The imaging experiment can be repeated by replacing standard balls with different sizes.
One embodiment of the calculation before fitting step S2 is:
the data fitting method mainly comprises the steps of calculating the numerical equivalent brightness of the fitting points and calculating the cosine of each input included angle of the BRDF. This should be considered in such a three-dimensional rectangular coordinate system: the origin is taken as the center of the sphere of the standard sphere, with the z axis pointing towards the camera, and the x and y axes are the same as the wide pixel growth direction (right) and the high pixel growth direction (down) of the photograph, respectively. Which is a left-handed coordinate system. Such a coordinate system that will vary with the camera position is both available and suitable, since the calculation of either BRDF or brightness is directly related to the pairwise angle of the respective directions and not to the coordinate system selection. The left-handed system is chosen for the convenience of extracting data from the image.
Because the distance between the camera and the standard ball is far larger than the diameter of the standard ball, the emergent light direction O can be approximately considered to be the forward direction of the z axis under the low precision requirement of the simulation level. The cosine of the included angle alpha between the opposite direction J of the main incident light and the emergent light can be obtained by utilizing the distance among the camera, the standard ball and the shadow recorded when each picture is shot:
Figure GDA0002795043560000071
where the corner marks b and a and S denote the standard sphere, camera and shadow, respectively, SsaRepresenting the distance between the shadow and the camera, SsbDenotes the distance between the standard sphere and the shadow, SabRepresenting the distance between the standard ball and the camera. Operation on arbitrary two directions U and V<U,V>The cosine of the included angle between the two is shown, but the cosine value is zero when the cosine value is negative.
Pixel radius R of a sphere0Center of circle pixel position<X0,Y0>Can be calculated by the following formula:
Figure GDA0002795043560000072
Figure GDA0002795043560000073
Figure GDA0002795043560000074
Figure GDA0002795043560000075
Figure GDA0002795043560000076
Figure GDA0002795043560000081
Figure GDA0002795043560000082
Figure GDA0002795043560000083
wherein (x)i,yi) Is the pixel location of the N boundary points taken from the edge of the great circle of the ball image on the photograph. After the N boundary points are located, the circle center and the radius are calculated such that the sum of the squares of the differences between the distances between the boundary points and the circle center and the radius is minimized.
Another angle β should be calculated in the respective (x, y) plane of each picture with respect to the opposite direction J of the incident chief ray, which is the azimuthal angle of J in the (x, y) plane, and ranges from (- π, π ], which is the angular distance from the x-axis direction to the projection direction of J in the (x, y) plane.
Figure GDA0002795043560000084
Note that all pixels within the image circle should be summed and that only pixels in the direction of the incoming light should not be considered. (x, y) is the pixel position, LnProportional to the brightness. The value is three-color gray level in visible light wave band; the infrared band is calculated by the Planck formula according to the preset emissivity of the thermal imager and the equivalent temperature of each pixel obtained by shooting.
For each pixel point (x, y) in the image circle, the cosine of the azimuth phi of the macroscopic normal direction Z and the included angle gamma between the azimuth phi and the O can be calculated as follows:
Figure GDA0002795043560000085
φ=atan2(y-Yo,x-Xo)
and comprises the following components: < J, Z > ═ cos α cos γ + sin α sin γ cos (β - φ)
The sine values in the above formula all take positive values since the invalid points where < U, V > is less than or equal to zero are discarded at any time during the actual calculation.
The micro-normal direction H, which is the mean average direction of the functions of both J and O directions, also has the relationship:
Figure GDA0002795043560000086
Figure GDA0002795043560000091
note that the above formula holds only for those pixels for which < U, V > is positive.
One embodiment of the fitting step S3 is as follows:
the fitting of the brightness value or three-color gray value L corresponding to the pixel point on the ball that meets the main light source in the picture should use the following analytical formula:
L=L0+L1+L2+L3+L4
Figure GDA0002795043560000092
Figure GDA0002795043560000093
Figure GDA0002795043560000094
Figure GDA0002795043560000095
Figure GDA0002795043560000096
wherein B (I, O, Z) is a parameterized formula of BRDF; i is the emergent light direction; t isa、TbTemperatures recorded for air and standard ball, respectively; p (-) is Planck's formula; kappa is an extinction coefficient; sabIs the shooting distance of the imaging device to the standard ball; c1For shading factor, when the main light source is turned on for shooting C11, shading shooting C1Taking 0; a. the0、A1、A2、A3And A4Are all scaling coefficients that can be determined by fitting. L is0Is the spontaneous emission of a standard sphere; l is1Primary source radiation reflected by a standard sphere; l is2Photographer radiation reflected off of a standard sphere; l is3Fixed dim background radiation reflected off of a standard sphere; l is4Is the spontaneous emission of air on the standard ball to imaging device path.
Because different wave bands are generally shot by different cameras, the parameter values obtained by actual fitting are all related to the wave bands and are equivalent values of the parameters. Although objective factors such as camera resolution and the like can affect the roughness of the internal parameters of the BRDF, the simulation application result also has the effect of influencing the camera resolution, so that the obtained equivalent values can be used in the actual simulation engineering.
Using the above analytical formula for fitting a numerical function Ln(x, y) the parameters A and κ are available, as well as the internal parameters of the BRDF. Saturated pixel data above the highest 255 picture intensities need to be discarded before fitting in the visible band.
< examples and Effect verification >
After the above experiments were performed on a certain coating in the visible and long infrared bands using a solar simulator as a main light source, parameter results and relative errors obtained by fitting experimental data using a data analysis software library ROOT developed by the european nuclear center are shown in tables 1 to 4.
The BRDF parameterization formula adopts a Torrance type structure followed by an open source simulation platform illusion four and an FDG function formula used by the same:
Figure GDA0002795043560000101
F(O,H)=F0+(1-F0)2(-5.55473<O,H>-6.98316<O,H>)
Figure GDA0002795043560000102
α=R2
G(I,O,H)=G1(I,H)G2(O,H)
Figure GDA0002795043560000103
Figure GDA0002795043560000104
Figure GDA0002795043560000105
wherein the metallic M, the roughness R, the spectral factor F0All have no dimension, and the value range is 0 to 1. Metallicity describes the proportion of metallic micro-elements; the roughness is used for controlling the roughness of the surface, and when the roughness is 0, the whole surface is closest to the mirror surface; the spectral factor represents the reflection ratio of light rays vertically incident to the surface, and when the reflection ratio is increased in a certain waveband, the light reflecting capacity of the material in the waveband is enhanced.
Dividing the tristimulus values for the visible band by 20 and multiplying the luminance values for the infrared band by 500 to approximate their magnitudes before actual fitting; the fitted per degree of freedom variance of such four bands is: blue 2.6; red 2.7; infrared 0.71. However, the values a in tables 1 to 4 are inverse operation results of the direct output results, and are original values whose magnitudes are not close to each other. It should be noted that, in order to prevent the parameters from exceeding the limits in the fitting process, the parameters which can only take positive values are subjected to exponential processing; for those parameters with values from 0 to 1, the arctan function is used to process the parameters before the formula is input. And the fitting parameter results and relative errors are also processed by the inverse transfer of these equations.
Table 1 λ 0.45 μm fitting results
Figure GDA0002795043560000111
Table 2 λ 0.55 μm fitting results
Figure GDA0002795043560000112
Table 3 λ 0.65 μm fitting results
Figure GDA0002795043560000113
Table 4 λ 10 μm fitting results
Figure GDA0002795043560000121
The relative error here refers to the relative error generated in the fitting process. Because the fitting relative error is very small, the early data acquisition error meets the requirement of simulation-level precision, and the final error superposition can lead to the parameter value being used for the visual simulation engineering application.
The material ball images were simulated using the phantom four simulation platform and the above partial parameter values as shown in fig. 2(a) to 2 (d). The infrared band has removed the self-luminescent coating in order to contain only the reflected light effect.
Although some specific embodiments of the present invention have been described in detail by way of examples, it should be understood by those skilled in the art that the above examples are for illustrative purposes only and are not intended to limit the scope of the present invention. It will be appreciated by those skilled in the art that modifications may be made to the above embodiments without departing from the scope and spirit of the invention. The scope of the invention is defined by the appended claims.

Claims (2)

1. A method for obtaining the simulation parameters of the bidirectional reflectance distribution function of a coating by an imaging method is characterized by comprising a measuring step, a calculating step before fitting and a fitting step, wherein,
the measuring step comprises:
placing the standard ball with the coating on the surface under a parallel light source to form a shadow;
imaging the standard ball for multiple times through the imaging device, and recording the distance between the imaging device, the standard ball and the shadow every time of imaging; the imaging device is an infrared imaging device;
the calculating step before fitting comprises:
calculating the cosine of an included angle between the reverse direction J of the incident light and the emergent light O according to the distance between the imaging equipment, the standard ball and the shadow; calculating the pixel position coordinates of the circle center according to the picture acquired by the imaging equipment; calculating the azimuth angle beta of the J in the picture plane; calculating the azimuth angle phi of the macroscopic normal direction Z of each pixel point in the image circle and the included angle gamma between Z and O;
the fitting step comprises:
the luminance value L is fitted by the following analytical formula:
L=L0+L1+L2+L3+L4
obtaining the metallic M, the roughness R and the spectral factor F0The fitting result of (1);
L0is the spontaneous emission of a standard sphere; l is1Primary source radiation reflected by a standard sphere; l is2Photographer radiation reflected off of a standard sphere; l is3Fixed dim background radiation reflected off of a standard sphere; l is4Spontaneous radiation of air on the path from a standard ball to the imaging device;
L0、L1、L2、L3and L4The calculation formula of (2) is as follows:
Figure FDA0002773746440000011
Figure FDA0002773746440000012
Figure FDA0002773746440000013
Figure FDA0002773746440000014
Figure FDA0002773746440000021
wherein B (-) is a parameterized formula for BRDF; t isa、TbTemperatures recorded for air and standard ball, respectively; p (-) is PlanckoFormula (I); kappa is an extinction coefficient; sabIs the shooting distance of the imaging device to the standard ball; c1For shading factor, when the main light source is turned on for shooting C11, shading shooting C1Taking 0; a. the0、A1、A2、A3And A4Are all scaling coefficients that can be determined by fitting.
2. The method for obtaining the simulation parameters of the bidirectional reflectance distribution function of the coating by the imaging method according to claim 1, wherein the parameterized formula of the BRDF is specifically formed as:
Figure FDA0002773746440000022
F(O,H)=F0+(1-F0)2(-5.55473<O,H>-6.98316<O,H>)
Figure FDA0002773746440000023
α=R2
G(I,O,H)=G1(I,H)G2(O,H)
Figure FDA0002773746440000024
Figure FDA0002773746440000025
Figure FDA0002773746440000026
wherein M is metallic and is used for describing the proportion of the metallic micro surface element; r is roughness, which is used for representing the roughness of the surface; f0Is a music scoreA factor characterizing the reflectance of light rays incident perpendicularly to the surface; h is the mean direction of the two directional functions J and O; and I is the emergent light direction.
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